An Ipsos Mori poll of more than 2,750 state school pupils found children from single-parent families are nearly three times as likely to say their family could not afford for them to be a student as those living in two-parent homes.
A third of children aged 11 to 16 from single-parent families voiced serious worries about the cost of university for their parents, compared with 13 per cent of pupils from two-parent homes, according to the survey commissioned by the Sutton Trust.
Older pupils are more likely to cite worries over "getting into debt" as a reason for saying they are unlikely to continue into higher education, with 29 per cent of those in school Years 10 and 11 citing debt as a barrier compared with 10 per cent of those in Year 7.
Almost two thirds of pupils also think highly selective universities are more expensive for students than other institutions, despite most universities charging close to £9,000 a year from next year.
Sir Peter Lampl, chairman of the Sutton Trust, said: "The government should think again about its fees and loans package. There is increasing evidence that the new fees are seen as too high, particularly by those on modest means.
"Ministers should consider means testing fees, so that merit not money is the key consideration in a young person's decision."
The report also found 81 per cent of all 11-16 year olds feel they are "very" or "fairly" likely to enter higher education, but this falls to 74 per cent for those from the least affluent families.
The findings follow last month's report by the Independent Commission on Fees, which said one teenager in 20 who would have been expected to apply to university in 2012 did not do so.
This equates to approximately 15,000 "missing" young applicants, though it added there was no "disproportionate drop-off in applications from poorer or less advantaged communities".
Liam Burns, president of the National Union of Students, said the new poll's finding confirmed fears about the impact of higher tuition fees.
"The student funding arrangements are hideously complicated, so I am hardly surprised that those from less affluent backgrounds are concerned," he said.
Meanwhile, the Russell Group of 24 research-intensive universities has launched a film urging students to think about which A-levels they choose and how it can affect their chances of attending highly selective institutions.
It recommends students take at least two of the following subjects: maths and further maths, physics, biology, chemistry, history, geography, modern and classical languages and English literature.
"All too often students disadvantage themselves by choosing a combination of subjects at A level which will not equip them with the right skills and knowledge for their preferred university course," said Wendy Piatt, director general of the Russell Group.
Informed Choices can be viewed on YouTube at http://youtu.be/54kKLOkoFxk.